Question

Question:
Using only a compass and a straightedge, you are constructing a line perpendicular to AB and passing through a given point, M, on AB. With a compass of set width, you have drawn arcs that intersect AB on each side of M and marked the two intersection points as P and Q.
Options:
-P and set its width to M
-M and set its width beyond P
-P and set its width beyond M
-M and set its width to half the distance between P and M

Answer 1

The construction goes with P and set its width to M.

The correct option is (A).

What is perpendicular bisector ?

A perpendicular bisector of a line segment is a line segment perpendicular to and passing through the midpoint of  figure.

Now, a line perpendicular to AB and passing through an external point M.

first step :Put the compass needle on M and, keep the compass width the same then draw two arcs that intersect AB.

Second step: After drawing arcs, from the intersecting points named P and Q.

Now, keeping the width of compass same as before and to the opposite side of M draw an arc named it as M'

Third step: Using straightedge draw line passes through M.

The lines which passes through M will be perpendicular to AB.

The above discussed are steps to draw perpendicular bisector of AB.

Learn more about this concept here:

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